Java Program Write a method that implements Ackermanns funct

Java Program:

Write a method that implements Ackermann\'s function:
Ack(x, y) = y + 1 when x = 0
Ack(x, y) = Ack(x - 1, 1) when x > 0 and y = 0
Ack(x, y) = A(x-1, A(x, y-1)   when x > 0 and y > 0

Use type long. Write a program that displays the value of Ack(n, n) for n = 0, 1, 2, ... For what calue of n is the value of Ack(n, n) too large for type long? Ackermann\'s function is famous because Ack(n,n) grows so rapidly with increasing n.

Solution

package chegg;

/* Ackermann function class */
public class Ack_function
{
   /* Ackermann function method take long X and Y*/
   public static long Ack(long X, long Y)
{
      
if(X==0)
{
   /* Ack(x, y) = y + 1 , when x = 0*/
return(Y + 1);
}
else    
if(X > 0 && Y == 0)
{
   /*Ack(x, y) = Ack(x - 1, 1) ,when x > 0 and y = 0*/
return (Ack(X-1,1));
}
else
if(X>0 && Y > 0);
{
   /*Ack(x, y) = A(x-1, A(x, y-1) , when x > 0 and y > 0*/
return (Ack(X-1, Ack(X,Y-1)));
}
}
   /* main method*/
   public static void main(String[] args)
   {
      
       /*print the value of Ack(n, n) where n=0,1,2*/
       for(int i=0;i<=2;i++)
       {
           for(int j=0;j<=2;j++)
           {
               System.out.println(\"Ack(\"+i+\",\" + j +\") is: \"+Ack(i, j));
           }
       }
      
         
      
   }

}//end of class

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output sample:-

Ack(0,0) is: 1
Ack(0,1) is: 2
Ack(0,2) is: 3
Ack(1,0) is: 2
Ack(1,1) is: 3
Ack(1,2) is: 4
Ack(2,0) is: 3
Ack(2,1) is: 5
Ack(2,2) is: 7

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If you have any query, please feel free to ask.

Thanks a lot.